3 papers
math.NT2025
A Minkowski-type theorem on distances to cusps: the general case
Mathieu Dutour
In a previous paper, we studied the connection between points in and -dimensional rigid adelic spaces on a totally real number field with class number $h_K =…
math.NT2025
A Minkowski-type theorem on distances to cusps: the class number one case
Mathieu Dutour
In the study of Euclidean lattices, the product of the successive minima is bounded from above and below by explicit quantities. This result is known as Minkowski's second theorem,…
math.RT2022
Infinite-rank Euclidean Lattices and Loop Groups
Mathieu Dutour, Manish M. Patnaik
In this paper, we associate a family of infinite-rank pro-Euclidean lattices to elements of a formal loop group and a highest weight representation of the underlying affine Kac--Mo…